How do you factor the trinomial $2x^2 + 3x + 1$ ?

Question

2126 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-03T07:59:27

$color(blue)((2x+1)(x+1)$

$2x^2+3x+1$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 2*1 = 2$

AND

$N_1 +N_2 = b = 3$

After trying out a few numbers we get:

$N_1 = 2$ and $N_2 =1$

$2*1 =2$ , and $2+1= 3$

$2x^2+color(blue)(3x)+1 = 2x^2+color(blue)(2x+1x)+1$

$=2x(x+1) +1(x+1)$

Here, $(x+1)$ is common to both terms ,

$=(2x+1)(x+1)$

So, the factorised form of the equation is :
$color(blue)((2x+1)(x+1)$

How do you factor the trinomial 2x^2 + 3x + 12x^2 + 3x + 1?